Definitions and discussions about printmaking techniques and materials can fill volumes, so what I have offered below is extremely abbreviated and just barely adequate to help answer your question.

The following are known as Relief Processes where the image is taken from the top surface of a block in which the design is carved or engraved with cutting tools (the parts not printed are cut or carved away). The block is then inked and printed onto paper or other media.

Woodcut or Woodblock Print: a print made from wood carved along the plank or grain side. The earliest known woodcuts date at least from the ninth century in China (they are images of the Buddha), although surviving examples are sophisticated enough to suggest that a developmental period of unknown duration must have preceded these surviving specimens.

Wood Engraving: a print made from woodblocks engraved on the end grain (blocks sawn across the grain).

The following are known as Intaglio Processes in which the image is made from the lower surface of an inked plate. The image is transferred onto paper under great pressure with a printing press, causing the ink held within the incised lines to transfer to the paper.

Etching: corroding lines, shapes, and textures into metal sheets (usually copper or zinc) with a solution of acid (referred to as a “mordant”) of varying formulas (typically including nitric acid, hydrochloric acid, or ferric chloride). The process of corrosion is called “biting.” The depth of the biting is controlled by the strength of the acid solution and the time it is allowed to bite into the metal plate. Typically the plate is first prepared with an acid resist ground (such as wax, gum, asphaltum, or resin) and then the design is drawn with a sharp etching tool through the resist. Thus the acid will bite into the plate only in those areas that were drawn (i.e., where the ground was removed with the etching needle). As the image is developed during the etching process, areas in need of correction or not intended to be printed as deeply as others can be “stopped out” with an acid resist varnish (such as a mixture of turpentine and asphaltum). The plates are then inked and printed to paper or other media.

Engraving: Incising lines, shapes, and textures into metal sheets or plates (wood, plastic, and glass can also be used) through the use of a hand-held incising tool called a “burin” or “graver.” The plates are then inked and printed to paper or other media. As engraving requires direct incision into the plate, the hand pressure required is greater than in etching through a soft wax ground. Thus engraving is generally a more resistant medium and the quality of line and shape is typically more controlled compared to that of etching in which the incising tool moves more freely through the acid-resist ground.

Drypoint: Incising, scoring, or scratching an image into a metal (or plastic) plate with a steel or diamond point. Drypoint lines wear out more quickly, as they are not as deep as are engraved or etched lines.

There are various other techniques and media used in Intaglio processes (including aquatint, lift or softground, mezzotint, roulette).

As for your referring to “hand etched,” I suppose you mean the basic etching technique, which is, as described above, a process of drawing through a wax ground to expose the lines for biting with acid. The printing, however, must be done with a press to exert the pressure required to transfer onto paper the ink held inside the etched lines. One cannot do that part of the process by hand.

Your reference to “hand colored” is not a strictly technical term and must indicate, I assume, that the color was applied by hand either to the printing block, printing plate, or already printed image. Hand coloring is quite common in the history of printmaking.

There are many books on these topics. A visit to any good library should satisfy your curiosity.